Transferring ownership of an asset is very easy to do through the action bar.
What does it mean to "transfer ownership?"
Transferring ownership means that you are changing the owner of that dataset. This is different from sharing a dataset, which shares the dataset with other users while retaining original ownership. For more information about sharing a dataset, read this article.
What rights do I need to have to transfer ownership?
You must be an Administrator on the site. Furthermore, the person to whom you are transferring ownership must have a role on the domain. If you are viewing another person's dataset you will also have the option to transfer ownership to yourself.
Transferring ownership of a published dataset is now done through the action bar. First, select "..." next to the Edit button and then Transfer Ownership.
This will open a modal where you can type in the name or email of the registered Data & Insights user you would like to transfer ownership of the asset. Once selected, select Transfer.